On the one hand, termination analysis of logic programs is now a fairly established research topic within the logic programming community. On the other hand, non-termination analysis seems to remain a much less attractive subject. If we divide this line of research into two kinds of approaches, dynamic versus static analysis, this paper belongs to the latter. It proposes a criterion for detecting non-terminating atomic queries with respect to binary constraint logic programming (CLP) rules, which strictly generalizes our previous works on this subject. We give a generic operational definition and an implemented logical form of this criterion. Then we show that the logical form is correct and complete with respect to the operational definition.

We consider a multiserver delay queue with finite additional waiting spaces and time-varying arrival rates, where the customers waiting in the buffer may abandon. These are features that arise naturally from the study of service systems such as call centers. Moreover, we assume rewards for successful service completions and cost rates for service resources. Finally, we consider service-level agreements that constrain both the fractions of callers who abandon and the ones who are blocked.

Applying the theory of Lagrangian mechanics to the fluid limit of a related Markovian service network model, we obtain near-profit-optimal staffing and provisioning schedules. The nature of this solution consists of three modes of operation. A key step in deriving this solution is combining the modified offered load approximation for loss systems with our fluid model. We use them to estimate effectively both our service-level agreement metrics and the profit for the original queuing model. Second-order profit improvements are achieved through a modified offered load version of the conventional square root safety rule.

We consider a two-queue model with state-dependent setups, in which a single server alternately serves the two queues. The high-priority queue is served exhaustively, whereas the low-priority queue is served according to the k-limited strategy. A setup at a queue is incurred only if there are customers waiting at the polled queue. We obtain the transforms of the queue length and sojourn time distributions under the assumption of Poisson arrivals, generally distributed service times, and generally distributed setup times. The interest for this model is fueled by an application in the field of logistics. It is shown how the results of this analysis can be applied in the evaluation of a stochastic two-item single-capacity production system. From these results we can conclude that significant cost reductions are possible by bounding the production runs of the low-priority item, which indicates the potential of the k-limited service discipline as priority rule in production environments.

We consider a network of parallel service stations each modeled as a single-server queue. Each station serves its own dedicated customers as well as generic customers who are routed from a central controller. We suppose that the cost incurred by a customer is an increasing function of her time spent in the system. In a significant advance on most previous work, we do not require waiting costs to be convex, still less linear. With the objective of minimizing the long-run average waiting cost, we develop two heuristic routing policies, one of which is based on dynamic programming policy improvement and the other on Lagrangian relaxation. In developing the latter policy, we show that each station is “indexable” under mild conditions for customers’ waiting costs and also prove some structural results on the admission control problem that naturally arises as a result of the Lagrangian relaxation. We then test the performance of our heuristics in an extensive numerical study and show that the Lagrangian heuristic demonstrates a strong level of performance in a range of traffic conditions. In particular, it clearly outperforms both a greedy heuristic, which is a standard proposal in complex routing problems, and a recent proposal from the heavy traffic literature.

In structural design of current complex mechanisms or robots like parallel kinematic machines (PKMs), surgical robots, and reconfigurable robots, there commonly exist some functional modules called complex joints (CJs). Each of them, consisting of several simple pairs and essentially a mechanism, plays the same and more important roles as simple joints in kinematics and dynamics. However, as the primarily important aspect in mechanism analysis, the type and mobility of these CJs are far from familiarity. Therefore, this paper aims at addressing the type and mobility of CJs. For this purpose, the concept and classification of CJs are first discussed, an effective method to analyze the mobility characteristics of these CJs is then developed based on the equivalent screw system. The advantage of this method is that it reveals mobility characteristics by using equivalent transformations of kinematic pair screw (KP-screw) and constraint screw (C-screw) systems. With this method, the mobility characteristics of some concrete CJs are obtained correspondingly.

We study the effects of different pricing strategies available to a production–inventory system with capacitated supply, which operates in a fluctuating demand environment. The demand depends on the environment and on the offered price. For such systems, three plausible pricing strategies are investigated: static pricing, for which only one price is used at all times, environment-dependent pricing, for which price changes with the environment, and dynamic pricing, for which price depends on both the current environment and the stock level. The objective is to find an optimal replenishment and pricing policy under each of these strategies. This article presents some structural properties of optimal replenishment policies and a numerical study that compares the performances of these three pricing strategies.

As a model for streaming multimedia applications, we study an unreliable retrial queue with infinite-capacity orbit and normal queue for which the retrial rate and the server repair rate are controllable. Customers join the retrial orbit if and only if their service is interrupted by a server failure. Interrupted customers do not rejoin the normal queue but repeatedly attempt to access the server at independent and identically distributed intervals until it is found functioning and idle. We provide stability conditions, queue length distributions, stochastic decomposition results, and performance measures. The joint optimization of the retrial and server repair rates is also studied.

In this article, we develop a simple method to approximate the transient behavior of queueing systems. In particular, it is shown how singularity analysis of a known generating function of a transient sequence of some performance measure leads to an approximation of this sequence. To illustrate our approach, several specific transient sequences are investigated in detail. By means of some numerical examples, we validate our approximations and demonstrate the usefulness of the technique.

We investigate the presence and impact of forecast errors in the arrival rate of customers to a service system. Analysis of a large dataset shows that forecast errors can be large relative to the fluctuations naturally expected in a Poisson process. We show that ignoring forecast errors typically leads to overestimates of performance and that forecast errors of the magnitude seen in our dataset can have a practically significant impact on predictions of long-run performance. We also define short-run performance as the random percentage of calls received in a particular period that are answered in a timely fashion. We prove a central limit theorem that yields a normal-mixture approximation for its distribution for Markovian queues and we sketch an argument that shows that a normal-mixture approximation should be valid in great generality. Our results provide motivation for studying staffing strategies that are more flexible than the fixed-level staffing rules traditionally studied in the literature.

This article offers an approach for studying the time-dependent occupancy distribution for a modest generalization of the GI/G/1 queuing system in which interarrival times and service times, although mutually independent, are not necessarily identically distributed. We develop and explore an analytical model leading to a computational approach that gives tight bounds on the occupancy distribution. Although there is no general closed-form characterization of probability law dynamics for occupancy in the GI/G/1 queue, our results offer what might be termed “near-closed-form” in that accurate plots of the transient occupancy distribution can be constructed with an insignificant computational burden. We believe that our results are unique; we are unaware of any alternative analytical approach leading to a numerical characterization of the time-dependent occupancy distribution for the G/G/1 queuing systems considered here.

Our analyses employ a marked point process that converges to the occupancy process at any fixed time t; it is shown that this process forms a Markov chain from which the transient occupancy law is available. We verify our analytical approach via comparison with the well-known closed-form expressions for time-dependent occupancy distribution of the M/M/1 queue. Additionally, we suggest the viability of our approach, as a computational means of obtaining the time-dependent occupancy distribution, through straightforward application to a Gamma[x]/Weibull/1 queuing system having batch arrivals and batch job services.

Numerous examples of real-time services arise in the service industry that can be modeled as loss systems. These include agent staffing for call centers, provisioning bandwidth for private line services, making rooms available for hotel reservations, and congestion pricing for parking spaces. Given that arriving customers make their decision to join the system based on the current service price, the manager can use price as a mechanism to control the utilization of the system. A major objective for the manager is then to find a pricing policy that maximizes total revenue while meeting the quality of service targets desired by the customers. For systems with growing demand and service capacity, we provide a dynamic pricing algorithm. A key feature of our solution is congestion pricing. We use demand forecasts to anticipate future service congestion and set the present price accordingly.

We show that many classical decision problems about1-counter ω-languages, context free ω-languages, or infinitary rational relations, are Π½ -complete, hence located at the second level of the analytical hierarchy, and “highly undecidable”.In particular, the universalityproblem, the inclusion problem, the equivalence problem, the determinizability problem, the complementability problem, and theunambiguity problem are all Π½ -complete for context-free ω-languages or for infinitary rational relations. Topological and arithmetical properties of1-counter ω-languages, context free ω-languages, or infinitary rational relations, are also highly undecidable.These very surprising results provide the first examples of highly undecidable problems about the behaviour of verysimple finite machines like 1-counter automata or 2-tapeautomata.

Embodiment design (ED) is an early phase of product development. ED problems consist of finding solution principles that satisfy product requirements such as physics behaviors and interactions between components. Constraint satisfaction techniques are useful to solve constraint-based models that are often partial, heterogeneous, and uncertain in ED. This paper proposes new constraint satisfaction techniques to tackle piecewise-defined physics phenomena or skill-based rules and multiple categories of variables arising in design applications. New search heuristics and a global piecewise constraint are introduced in the branch and prune framework. The capabilities of these techniques are illustrated with both academic and real-world problems. Complete models of the latter are presented.

A selection method to support adaptive reuse of parametric finite element analysis (FEA) models is introduced in this paper. Adaptive reuse of engineering artifacts such as FEA models is common in product design, but difficult to automate because of the need to integrate new information. The proposed method factors reusability into selection by evaluating models based on comparative estimates of effort involved in adapting them for reuse to model a query problem. The method is developed for FEA models of component-based designs. FEA modeling of electronic chip packages is used to illustrate the method's usefulness. We conclude with a discussion on the method's advantages and limitations and highlight important issues for further research.

This research proposes a procedure for solving the multiresponse problem in the Taguchi method utilizing two data envelopment analysis (DEA) approaches, including comparisons of efficiency between different systems (CEBDS) and bilateral comparisons. In this procedure, each experiment in Taguchi's orthogonal array (OA) is treated as a decision-making unit (DMU) with the multiresponses as the inputs and outputs for all DMUs. For each factor of OA, the DMUs are divided into groups, each at the same factor level. Then, DMU's efficiency is separately evaluated by the CEBDS approach and the bilateral comparisons approach for each factor. The level efficiency, or the average of the efficiencies obtained by the CEBDS and the bilateral comparisons approaches for that factor level, is then used to determine the optimal factor levels for multiresponses. Three case studies are provided for illustration; in all, the proposed procedure provides the largest total anticipated improvements. Hence, it should be considered the most effective among all approaches applied in the case studies, including principal component analysis, DEA-based ranking approach, and others. In addition, the proposed procedure is more effective and requires less computational effort when the DMU's efficiency is evaluated by the bilateral comparisons approach instead of the CEBDS approach. In conclusion, the proposed procedure will provide great assistance to practitioners for solving the multiresponse problems in manufacturing applications on the Taguchi method.